unit root tests: trend included for bounded series X lies in a 0,100 interval and i want to check if X has a unit root. 
In (A)DF, and PP unit root tests one can have an intercept and/or a trend (in addition to the level and difference X lags). But if the series is naturally bounded, does it make sense to have both an intercept and trend? Thanks! 
 A: Strictly speaking, if your variable is bounded, it cannot have a unit root to begin with (let alone a unit root plus drift or plus trend). A unit root process is not bounded and can wander off arbitrarily far away from the initial point. Its increments are random.
Nonetheless, some persistent economic variables (interest rates, unemployment rate, etc.) are sometimes treated as unit-root processes even though they clearly are bounded (interest rates cannot be strongly negative; unemployment rate is roughly a percentage).
Then you may also ask, can they have drift or trend terms. Perhaps in relatively short periods there can be drifts, that is, deterministic linear trends; in sufficiently long periods a drift would violate the bounds, so then it is less likely.
Meanwhile, "trends" in unit root tests mean deterministic quadratic trends in the original data. Sometimes such patterns can be rejected by subject-matter reasoning. Anyway, a quadratic trend would also violate the bounds in a sufficiently long period, so they are plausible only in short periods.
Another way of thinking about a persistent variable that is bounded could be identifying two (or more) regimes:
(1) when the process is close to the bound, it tends to go away from the bound (up from 0 or down from 100 as in your example);
(2) when the process is far from the bound, it tends to behave as a unit-root process.
A threshold between what is "close" and what is "far" can be estimated.
